In a large pot or Dutch oven, heat oil over medium low heat. Add leeks and sauté until soft, about 4-5 minutes; add garlic, carrots and yellow pepper and sauté about 2-3 minutes.
Add corned beef, peppercorns or seasoning packet that comes with the corned beef, bay leaves, parsley and water; cover and bring to a boil. Simmer covered on low heat for 3 hours, until the meat becomes tender.
Remove the corned beef, set it on a cutting board and shred with a fork. Return it to the pot then add the cabbage and potatoes, taste for salt and pepper and adjust as needed. Cook until the potatoes and cabbage are tender, about 45 more minutes.